Defining parameters
Level: | \( N \) | = | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(73920\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(667))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 19096 | 18933 | 163 |
Cusp forms | 17865 | 17797 | 68 |
Eisenstein series | 1231 | 1136 | 95 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
667.2.a | \(\chi_{667}(1, \cdot)\) | 667.2.a.a | 10 | 1 |
667.2.a.b | 12 | |||
667.2.a.c | 13 | |||
667.2.a.d | 16 | |||
667.2.c | \(\chi_{667}(231, \cdot)\) | 667.2.c.a | 24 | 1 |
667.2.c.b | 30 | |||
667.2.f | \(\chi_{667}(505, \cdot)\) | 667.2.f.a | 12 | 2 |
667.2.f.b | 104 | |||
667.2.g | \(\chi_{667}(24, \cdot)\) | 667.2.g.a | 6 | 6 |
667.2.g.b | 144 | |||
667.2.g.c | 186 | |||
667.2.h | \(\chi_{667}(59, \cdot)\) | 667.2.h.a | 280 | 10 |
667.2.h.b | 280 | |||
667.2.j | \(\chi_{667}(93, \cdot)\) | 667.2.j.a | 144 | 6 |
667.2.j.b | 180 | |||
667.2.m | \(\chi_{667}(144, \cdot)\) | 667.2.m.a | 580 | 10 |
667.2.o | \(\chi_{667}(68, \cdot)\) | 667.2.o.a | 72 | 12 |
667.2.o.b | 624 | |||
667.2.q | \(\chi_{667}(17, \cdot)\) | 667.2.q.a | 1160 | 20 |
667.2.s | \(\chi_{667}(16, \cdot)\) | 667.2.s.a | 3480 | 60 |
667.2.u | \(\chi_{667}(4, \cdot)\) | 667.2.u.a | 3480 | 60 |
667.2.x | \(\chi_{667}(10, \cdot)\) | 667.2.x.a | 6960 | 120 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(667))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)